TESTING/EIG/zchkhs.f(3)

NAME
TESTING/EIG/zchkhs.f

SYNOPSIS

  Functions/Subroutines
subroutine zchkhs (nsizes, nn, ntypes, dotype, iseed, thresh, nounit, a, lda, h, t1, t2, u, ldu, z, uz, w1, w3, evectl, evectr, evecty, evectx, uu, tau, work, nwork, rwork, iwork, select, result, info)
ZCHKHS

Function/Subroutine Documentation

  subroutine zchkhs (integer nsizes, integer, dimension( * ) nn, integer ntypes, logical, dimension( * ) dotype, integer, dimension( 4 ) iseed, double precision thresh, integer nounit, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( lda, * ) h, complex*16, dimension( lda, * ) t1, complex*16, dimension( lda, * ) t2, complex*16, dimension( ldu, * ) u, integer ldu, complex*16, dimension( ldu, * ) z, complex*16, dimension( ldu, * ) uz, complex*16, dimension( * ) w1, complex*16, dimension( * ) w3, complex*16, dimension( ldu, * ) evectl, complex*16, dimension( ldu, * ) evectr, complex*16, dimension( ldu, * ) evecty, complex*16, dimension( ldu, * ) evectx, complex*16, dimension( ldu, * ) uu, complex*16, dimension( * ) tau, complex*16, dimension( * ) work, integer nwork, double precision, dimension( * ) rwork, integer, dimension( * ) iwork, logical, dimension( * ) select, double precision, dimension( 16 ) result, integer info)

ZCHKHS

Purpose:

    !>
    !>    ZCHKHS  checks the nonsymmetric eigenvalue problem routines.
    !>
    !>            ZGEHRD factors A as  U H U' , where ' means conjugate
    !>            transpose, H is hessenberg, and U is unitary.
    !>
    !>            ZUNGHR generates the unitary matrix U.
    !>
    !>            ZUNMHR multiplies a matrix by the unitary matrix U.
    !>
    !>            ZHSEQR factors H as  Z T Z' , where Z is unitary and T
    !>            is upper triangular.  It also computes the eigenvalues,
    !>            w(1), ..., w(n); we define a diagonal matrix W whose
    !>            (diagonal) entries are the eigenvalues.
    !>
    !>            ZTREVC computes the left eigenvector matrix L and the
    !>            right eigenvector matrix R for the matrix T.  The
    !>            columns of L are the complex conjugates of the left
    !>            eigenvectors of T.  The columns of R are the right
    !>            eigenvectors of T.  L is lower triangular, and R is
    !>            upper triangular.
    !>
    !>            ZHSEIN computes the left eigenvector matrix Y and the
    !>            right eigenvector matrix X for the matrix H.  The
    !>            columns of Y are the complex conjugates of the left
    !>            eigenvectors of H.  The columns of X are the right
    !>            eigenvectors of H.  Y is lower triangular, and X is
    !>            upper triangular.
    !>
    !>            ZTREVC3 computes left and right eigenvector matrices
    !>            from a Schur matrix T and backtransforms them with Z
    !>            to eigenvector matrices L and R for A. L and R are
    !>            GE matrices.
    !>
    !>    When ZCHKHS is called, a number of matrix  () and a
    !>    number of matrix  are specified.  For each size ()
    !>    and each type of matrix, one matrix will be generated and used
    !>    to test the nonsymmetric eigenroutines.  For each matrix, 16
    !>    tests will be performed:
    !>
    !>    (1)     | A - U H U**H | / ( |A| n ulp )
    !>
    !>    (2)     | I - UU**H | / ( n ulp )
    !>
    !>    (3)     | H - Z T Z**H | / ( |H| n ulp )
    !>
    !>    (4)     | I - ZZ**H | / ( n ulp )
    !>
    !>    (5)     | A - UZ H (UZ)**H | / ( |A| n ulp )
    !>
    !>    (6)     | I - UZ (UZ)**H | / ( n ulp )
    !>
    !>    (7)     | T(Z computed) - T(Z not computed) | / ( |T| ulp )
    !>
    !>    (8)     | W(Z computed) - W(Z not computed) | / ( |W| ulp )
    !>
    !>    (9)     | TR - RW | / ( |T| |R| ulp )
    !>
    !>    (10)    | L**H T - W**H L | / ( |T| |L| ulp )
    !>
    !>    (11)    | HX - XW | / ( |H| |X| ulp )
    !>
    !>    (12)    | Y**H H - W**H Y | / ( |H| |Y| ulp )
    !>
    !>    (13)    | AX - XW | / ( |A| |X| ulp )
    !>
    !>    (14)    | Y**H A - W**H Y | / ( |A| |Y| ulp )
    !>
    !>    (15)    | AR - RW | / ( |A| |R| ulp )
    !>
    !>    (16)    | LA - WL | / ( |A| |L| ulp )
    !>
    !>    The  are specified by an array NN(1:NSIZES); the value of
    !>    each element NN(j) specifies one size.
    !>    The  are specified by a logical array DOTYPE( 1:NTYPES );
    !>    if DOTYPE(j) is .TRUE., then matrix type  will be generated.
    !>    Currently, the list of possible types is:
    !>
    !>    (1)  The zero matrix.
    !>    (2)  The identity matrix.
    !>    (3)  A (transposed) Jordan block, with 1's on the diagonal.
    !>
    !>    (4)  A diagonal matrix with evenly spaced entries
    !>         1, ..., ULP  and random complex angles.
    !>         (ULP = (first number larger than 1) - 1 )
    !>    (5)  A diagonal matrix with geometrically spaced entries
    !>         1, ..., ULP  and random complex angles.
    !>    (6)  A diagonal matrix with  entries 1, ULP, ..., ULP
    !>         and random complex angles.
    !>
    !>    (7)  Same as (4), but multiplied by SQRT( overflow threshold )
    !>    (8)  Same as (4), but multiplied by SQRT( underflow threshold )
    !>
    !>    (9)  A matrix of the form  U' T U, where U is unitary and
    !>         T has evenly spaced entries 1, ..., ULP with random complex
    !>         angles on the diagonal and random O(1) entries in the upper
    !>         triangle.
    !>
    !>    (10) A matrix of the form  U' T U, where U is unitary and
    !>         T has geometrically spaced entries 1, ..., ULP with random
    !>         complex angles on the diagonal and random O(1) entries in
    !>         the upper triangle.
    !>
    !>    (11) A matrix of the form  U' T U, where U is unitary and
    !>         T has  entries 1, ULP,..., ULP with random
    !>         complex angles on the diagonal and random O(1) entries in
    !>         the upper triangle.
    !>
    !>    (12) A matrix of the form  U' T U, where U is unitary and
    !>         T has complex eigenvalues randomly chosen from
    !>         ULP < |z| < 1   and random O(1) entries in the upper
    !>         triangle.
    !>
    !>    (13) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has evenly spaced entries 1, ..., ULP
    !>         with random complex angles on the diagonal and random O(1)
    !>         entries in the upper triangle.
    !>
    !>    (14) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has geometrically spaced entries
    !>         1, ..., ULP with random complex angles on the diagonal
    !>         and random O(1) entries in the upper triangle.
    !>
    !>    (15) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has  entries 1, ULP,..., ULP
    !>         with random complex angles on the diagonal and random O(1)
    !>         entries in the upper triangle.
    !>
    !>    (16) A matrix of the form  X' T X, where X has condition
    !>         SQRT( ULP ) and T has complex eigenvalues randomly chosen
    !>         from   ULP < |z| < 1   and random O(1) entries in the upper
    !>         triangle.
    !>
    !>    (17) Same as (16), but multiplied by SQRT( overflow threshold )
    !>    (18) Same as (16), but multiplied by SQRT( underflow threshold )
    !>
    !>    (19) Nonsymmetric matrix with random entries chosen from |z| < 1
    !>    (20) Same as (19), but multiplied by SQRT( overflow threshold )
    !>    (21) Same as (19), but multiplied by SQRT( underflow threshold )
    !>

    !>  NSIZES - INTEGER
    !>           The number of sizes of matrices to use.  If it is zero,
    !>           ZCHKHS does nothing.  It must be at least zero.
    !>           Not modified.
    !>
    !>  NN     - INTEGER array, dimension (NSIZES)
    !>           An array containing the sizes to be used for the matrices.
    !>           Zero values will be skipped.  The values must be at least
    !>           zero.
    !>           Not modified.
    !>
    !>  NTYPES - INTEGER
    !>           The number of elements in DOTYPE.   If it is zero, ZCHKHS
    !>           does nothing.  It must be at least zero.  If it is MAXTYP+1
    !>           and NSIZES is 1, then an additional type, MAXTYP+1 is
    !>           defined, which is to use whatever matrix is in A.  This
    !>           is only useful if DOTYPE(1:MAXTYP) is .FALSE. and
    !>           DOTYPE(MAXTYP+1) is .TRUE. .
    !>           Not modified.
    !>
    !>  DOTYPE - LOGICAL array, dimension (NTYPES)
    !>           If DOTYPE(j) is .TRUE., then for each size in NN a
    !>           matrix of that size and of type j will be generated.
    !>           If NTYPES is smaller than the maximum number of types
    !>           defined (PARAMETER MAXTYP), then types NTYPES+1 through
    !>           MAXTYP will not be generated.  If NTYPES is larger
    !>           than MAXTYP, DOTYPE(MAXTYP+1) through DOTYPE(NTYPES)
    !>           will be ignored.
    !>           Not modified.
    !>
    !>  ISEED  - INTEGER array, dimension (4)
    !>           On entry ISEED specifies the seed of the random number
    !>           generator. The array elements should be between 0 and 4095;
    !>           if not they will be reduced mod 4096.  Also, ISEED(4) must
    !>           be odd.  The random number generator uses a linear
    !>           congruential sequence limited to small integers, and so
    !>           should produce machine independent random numbers. The
    !>           values of ISEED are changed on exit, and can be used in the
    !>           next call to ZCHKHS to continue the same random number
    !>           sequence.
    !>           Modified.
    !>
    !>  THRESH - DOUBLE PRECISION
    !>           A test will count as  if the , computed as
    !>           described above, exceeds THRESH.  Note that the error
    !>           is scaled to be O(1), so THRESH should be a reasonably
    !>           small multiple of 1, e.g., 10 or 100.  In particular,
    !>           it should not depend on the precision (single vs. double)
    !>           or the size of the matrix.  It must be at least zero.
    !>           Not modified.
    !>
    !>  NOUNIT - INTEGER
    !>           The FORTRAN unit number for printing out error messages
    !>           (e.g., if a routine returns IINFO not equal to 0.)
    !>           Not modified.
    !>
    !>  A      - COMPLEX*16 array, dimension (LDA,max(NN))
    !>           Used to hold the matrix whose eigenvalues are to be
    !>           computed.  On exit, A contains the last matrix actually
    !>           used.
    !>           Modified.
    !>
    !>  LDA    - INTEGER
    !>           The leading dimension of A, H, T1 and T2.  It must be at
    !>           least 1 and at least max( NN ).
    !>           Not modified.
    !>
    !>  H      - COMPLEX*16 array, dimension (LDA,max(NN))
    !>           The upper hessenberg matrix computed by ZGEHRD.  On exit,
    !>           H contains the Hessenberg form of the matrix in A.
    !>           Modified.
    !>
    !>  T1     - COMPLEX*16 array, dimension (LDA,max(NN))
    !>           The Schur (=) matrix computed by ZHSEQR
    !>           if Z is computed.  On exit, T1 contains the Schur form of
    !>           the matrix in A.
    !>           Modified.
    !>
    !>  T2     - COMPLEX*16 array, dimension (LDA,max(NN))
    !>           The Schur matrix computed by ZHSEQR when Z is not computed.
    !>           This should be identical to T1.
    !>           Modified.
    !>
    !>  LDU    - INTEGER
    !>           The leading dimension of U, Z, UZ and UU.  It must be at
    !>           least 1 and at least max( NN ).
    !>           Not modified.
    !>
    !>  U      - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The unitary matrix computed by ZGEHRD.
    !>           Modified.
    !>
    !>  Z      - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The unitary matrix computed by ZHSEQR.
    !>           Modified.
    !>
    !>  UZ     - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The product of U times Z.
    !>           Modified.
    !>
    !>  W1     - COMPLEX*16 array, dimension (max(NN))
    !>           The eigenvalues of A, as computed by a full Schur
    !>           decomposition H = Z T Z'.  On exit, W1 contains the
    !>           eigenvalues of the matrix in A.
    !>           Modified.
    !>
    !>  W3     - COMPLEX*16 array, dimension (max(NN))
    !>           The eigenvalues of A, as computed by a partial Schur
    !>           decomposition (Z not computed, T only computed as much
    !>           as is necessary for determining eigenvalues).  On exit,
    !>           W3 contains the eigenvalues of the matrix in A, possibly
    !>           perturbed by ZHSEIN.
    !>           Modified.
    !>
    !>  EVECTL - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The conjugate transpose of the (upper triangular) left
    !>           eigenvector matrix for the matrix in T1.
    !>           Modified.
    !>
    !>  EVEZTR - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The (upper triangular) right eigenvector matrix for the
    !>           matrix in T1.
    !>           Modified.
    !>
    !>  EVECTY - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The conjugate transpose of the left eigenvector matrix
    !>           for the matrix in H.
    !>           Modified.
    !>
    !>  EVECTX - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           The right eigenvector matrix for the matrix in H.
    !>           Modified.
    !>
    !>  UU     - COMPLEX*16 array, dimension (LDU,max(NN))
    !>           Details of the unitary matrix computed by ZGEHRD.
    !>           Modified.
    !>
    !>  TAU    - COMPLEX*16 array, dimension (max(NN))
    !>           Further details of the unitary matrix computed by ZGEHRD.
    !>           Modified.
    !>
    !>  WORK   - COMPLEX*16 array, dimension (NWORK)
    !>           Workspace.
    !>           Modified.
    !>
    !>  NWORK  - INTEGER
    !>           The number of entries in WORK.  NWORK >= 4*NN(j)*NN(j) + 2.
    !>
    !>  RWORK  - DOUBLE PRECISION array, dimension (max(NN))
    !>           Workspace.  Could be equivalenced to IWORK, but not SELECT.
    !>           Modified.
    !>
    !>  IWORK  - INTEGER array, dimension (max(NN))
    !>           Workspace.
    !>           Modified.
    !>
    !>  SELECT - LOGICAL array, dimension (max(NN))
    !>           Workspace.  Could be equivalenced to IWORK, but not RWORK.
    !>           Modified.
    !>
    !>  RESULT - DOUBLE PRECISION array, dimension (16)
    !>           The values computed by the fourteen tests described above.
    !>           The values are currently limited to 1/ulp, to avoid
    !>           overflow.
    !>           Modified.
    !>
    !>  INFO   - INTEGER
    !>           If 0, then everything ran OK.
    !>            -1: NSIZES < 0
    !>            -2: Some NN(j) < 0
    !>            -3: NTYPES < 0
    !>            -6: THRESH < 0
    !>            -9: LDA < 1 or LDA < NMAX, where NMAX is max( NN(j) ).
    !>           -14: LDU < 1 or LDU < NMAX.
    !>           -26: NWORK too small.
    !>           If  ZLATMR, CLATMS, or CLATME returns an error code, the
    !>               absolute value of it is returned.
    !>           If 1, then ZHSEQR could not find all the shifts.
    !>           If 2, then the EISPACK code (for small blocks) failed.
    !>           If >2, then 30*N iterations were not enough to find an
    !>               eigenvalue or to decompose the problem.
    !>           Modified.
    !>
    !>-----------------------------------------------------------------------
    !>
    !>     Some Local Variables and Parameters:
    !>     ---- ----- --------- --- ----------
    !>
    !>     ZERO, ONE       Real 0 and 1.
    !>     MAXTYP          The number of types defined.
    !>     MTEST           The number of tests defined: care must be taken
    !>                     that (1) the size of RESULT, (2) the number of
    !>                     tests actually performed, and (3) MTEST agree.
    !>     NTEST           The number of tests performed on this matrix
    !>                     so far.  This should be less than MTEST, and
    !>                     equal to it by the last test.  It will be less
    !>                     if any of the routines being tested indicates
    !>                     that it could not compute the matrices that
    !>                     would be tested.
    !>     NMAX            Largest value in NN.
    !>     NMATS           The number of matrices generated so far.
    !>     NERRS           The number of tests which have exceeded THRESH
    !>                     so far (computed by DLAFTS).
    !>     COND, CONDS,
    !>     IMODE           Values to be passed to the matrix generators.
    !>     ANORM           Norm of A; passed to matrix generators.
    !>
    !>     OVFL, UNFL      Overflow and underflow thresholds.
    !>     ULP, ULPINV     Finest relative precision and its inverse.
    !>     RTOVFL, RTUNFL,
    !>     RTULP, RTULPI   Square roots of the previous 4 values.
    !>
    !>             The following four arrays decode JTYPE:
    !>     KTYPE(j)        The general type (1-10) for type .
    !>     KMODE(j)        The MODE value to be passed to the matrix
    !>                     generator for type .
    !>     KMAGN(j)        The order of magnitude ( O(1),
    !>                     O(overflow^(1/2) ), O(underflow^(1/2) )
    !>     KCONDS(j)       Selects whether CONDS is to be 1 or
    !>                     1/sqrt(ulp).  (0 means irrelevant.)
    !>

Author
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Definition at line 416 of file zchkhs.f.

Author

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